Probabilistic climate emulation with physics-constrained Gaussian processes

Emulators, or reduced complexity climate models, are surrogate Earth system models that produce projections of key climate quantities with minimal computational resources. Using time-series modeling or more advanced machine learning techniques, statistically-driven emulators have emerged as a promising venue, producing spatially resolved climate responses that are visually indistinguishable from state-of-the-art Earth system models. Yet, their lack of physical interpretability limits their wider adoption. In fact, the exploration of future emission scenarios still relies on one-dimensional energy balance models which can lack the flexibility to capture certain climate responses.

Here, we propose a statistically-driven emulator that hinges on an energy balance model. Using Gaussian processes, we formulate an emulator of temperature response that exactly satisfies the physical thermal response equations of an energy balance model. The result is an emulator that (1) enjoys the flexibility of statistical machine learning models and can be fitted against observations to produce spatially-resolved predictions (2) has physically-interpretable parameters that can be used to make inference about the climate system. This model shows skilfull prediction of annual mean global distribution of temperature, even over scenarios outside the range of observed emissions of greenhouse gases and aerosols during training — improvement in RMSE of 27% against the energy balance model and of 60% against a physics-free machine learning model. In addition, the Bayesian nature of our formulation provides a principled way to perform uncertainty quantification on the predictions.

We outline how the probabilistic nature of this emulator makes it a natural candidate for detection and attribution studies and discuss extension to a precipitation emulator also incorporating physical constraints. We hope that by combining the ability of machine learning techniques to capture complex patterns with the interpretability of energy balance models, our work will produce a reliable tool for efficiently and accurately exploring future climates.